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ÖRNEKLEME
METODLARI
If you survey every person or a whole set of units in
a population you are taking a census. However, this method is often
impracticable; as it’s often very costly in terms of time and money. For
example, a survey that asks complicated questions may need to use trained
interviewers to ensure questions are understood. This may be too expensive
if every person in the population is to be included.
Sometimes taking a census can be impossible. For example, a car
manufacturer might want to test the strength of cars being produced.
Obviously, each car could not be crash tested to determine its strength!
To overcome these problems, samples are taken from populations, and
estimates made about the total population based on information derived from
the sample. A sample must be large enough to give a good representation
of the population, but small enough to be manageable. In this section the
two major types of sampling, random and non-random, will be examined.
RANDOM SAMPLING
In random sampling, all items have some chance of selection that can be
calculated. Random sampling technique ensures that bias (see: page
179) is not introduced regarding who is included in the survey. Five common
random sampling techniques are:
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- simple
random sampling,
- systematic
sampling,
- stratified
sampling,
- cluster
sampling, and
- multi-stage sampling.
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SIMPLE RANDOM SAMPLING
With simple random sampling, each item in a population has an equal chance
of inclusion in the sample. For example, each name in a telephone book
could be numbered sequentially. If the sample size was to include 2,000
people, then 2,000 numbers could be randomly generated by computer or
numbers could be picked out of a hat. These numbers could then be matched
to names in the telephone book, thereby providing a list of 2,000 people.
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A Tattslotto draw is a good example of simple
random sampling. A sample of 6 numbers is randomly generated from a
population of 45, with each number having an equal chance of being
selected.
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The advantage of simple random sampling is that it is simple and
easy to apply when small populations are involved. However, because every
person or item in a population has to be listed before the corresponding
random numbers can be read, this method is very cumbersome to use for large
populations.
SYSTEMATIC SAMPLING
Systematic sampling, sometimes called interval sampling, means that there
is a gap, or interval, between each selection. This method is often used in
industry, where an item is selected for testing from a production line
(say, every fifteen minutes) to ensure that machines and equipment are
working to specification.
Alternatively, the manufacturer might decide to select every 20th item on a
production line to test for defects and quality. This technique requires
the first item to be selected at random as a starting point for testing
and, thereafter, every 20th item is chosen.
This technique could also be used when questioning people in a sample
survey. A market researcher might select every 10th person who enters a
particular store, after selecting a person at random as a starting point;
or interview occupants of every 5th house in a street, after selecting a
house at random as a starting point.
It may be that a researcher wants to select a fixed size sample. In this
case, it is first necessary to know the whole population size from which
the sample is being selected. The appropriate sampling interval, I,
is then calculated by dividing population size, N, by required sample size,
n, as follows:
ÖRNEK
If a systematic sample of 500 students were to be carried out in a
university with an enrolled population of 10,000, the sampling interval
would be:
Note: if I is
not a whole number, then it is rounded to the nearest whole number.
All students would be assigned sequential numbers. The starting point would
be chosen by selecting a random number between 1 and 20. If this number was
9, then the 9th student on the list of students would be selected along
with every following 20th student. The sample of students would be those
corresponding to student numbers 9, 29, 49, 69, ........ 9929, 9949, 9969
and 9989.
The advantage of systematic sampling is that it is simpler to select one
random number and then every ‘Ith’ (e.g. 20th) member on the list, than to
select as many random numbers as sample size. It also gives a good spread
right across the population. A disadvantage is that you may need a list to
start with, if you wish to know your sample size and calculate your
sampling interval.
STRATIFIED SAMPLING
A general problem with random sampling is that you could, by chance, miss
out a particular group in the sample. However, if you form the population
into groups, and sample from each group, you can make sure the sample is
representative.
In stratified sampling, the population is divided into groups called
strata. A sample is then drawn from within these strata. Some examples of
strata commonly used by the ABS are States, Age and Sex. Other strata may
be religion, academic ability or marital status.
ÖRNEK
- The committee of a school of 1,000
students wishes to assess any reaction to the re-introduction of
Pastoral Care into the school timetable. To ensure a
representative sample of students from all year levels, the
committee uses the stratified sampling technique.
In this case the strata are the year levels. Within each strata
the committee selects a sample. So, in a sample of 100 students,
all year levels would be included. The students in the sample
would be selected using simple random sampling or systematic
sampling within each strata
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Stratification is most useful when the stratifying variables are
simple to work with, easy to observe and closely related to the topic of
the survey.
An important aspect of stratification is that it can be used to select more
of one group than another. You may do this if you feel that responses are
more likely to vary in one group than another. So, if you know everyone in
one group has much the same value, you only need a small sample to get
information for that group; whereas in another group, the values may differ
widely and a bigger sample is needed.
If you want to combine group level information to get an answer for the
whole population, you have to take account of what proportion you selected
from each group (see ‘Bias in Estimation’ on page 186).
CLUSTER SAMPLING
It is sometimes expensive to spread your sample across the population as a
whole. For example, travel can become expensive if you are using
interviewers to travel between people spread all over the country. To
reduce costs you may choose a cluster sampling technique.
Cluster sampling divides the population into groups, or clusters. A number
of clusters are selected randomly to represent the population, and then all
units within selected clusters are included in the sample. No units from
non-selected clusters are included in the sample. They are represented by
those from selected clusters. This differs from stratified sampling, where
some units are selected from each group.
Examples of clusters may be factories, schools and geographic areas such as
electoral sub-divisions. The selected clusters are then used to represent
the population.
ÖRNEK
- Suppose an organisation wishes to find out
which sports Year 11 students are participating in across Australia.
It would be too costly and take too long to survey every student,
or even some students from every school. Instead, 100 schools are
randomly selected from all over Australia.
These schools are considered to be clusters. Then, every Year 11
student in these 100 schools is surveyed. In effect, students in
the sample of 100 schools represent all Year 11 students in Australia.
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Cluster sampling has several
advantages: reduced costs, simplified field work and administration is more
convenient. Instead of having a sample scattered over the entire coverage
area, the sample is more localised in relatively few centres (clusters).
Cluster sampling’s disadvantage is that less accurate results are often
obtained due to higher sampling error than for simple random sampling with
the same sample size. In the above example, you might expect to get more
accurate estimates from randomly selecting students across all schools than
from randomly selecting 100 schools and taking every student in those
chosen.
MULTI-STAGE SAMPLING
Multi-stage sampling is like cluster sampling, but involves selecting a
sample within each chosen cluster, rather than including all units in the
cluster. Thus, multi-stage sampling involves selecting a sample in at least
two stages. In the first stage, large groups or clusters are selected.
These clusters are designed to contain more population units than are required
for the final sample.
In the second stage,
population units are chosen from selected clusters to derive a final
sample. If more than two stages are used, the process of choosing
population units within clusters continues until the final sample is
achieved.
ÖRNEK
- An example of multi-stage sampling is
where, firstly, electoral sub-divisions (clusters) are sampled
from a city or state. Secondly, blocks of houses are selected from
within the electoral sub-divisions and, thirdly, individual houses
are selected from within the selected blocks of houses.
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The advantages of multi-stage sampling are convenience, economy and
efficiency. Multi-stage sampling does not require a complete list of
members in the target population, which greatly reduces sample preparation
cost. The list of members is required only for those clusters used in the
final stage. The main disadvantage of multi-stage sampling is the same as
for cluster sampling: lower accuracy due to higher sampling error
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:
ve 
olarak adlandırılır ve
anakütlenin merkezi eğiliminin nasıl olduğunu bu parametreler belirler. N ilede
anakütlenin genişliğini belirleriz.
ve örnek standard sapması S olacak şekilde rakamsal olarak da
gösterilebilinir. Bu gözlemlemde n nekadar geniş olursa 
) anakütle parametrelerinin belirli komşuluğunda olması ile
ilgili ihtimaller belirlememize yardimci olur.
=0.(0,5)+1.(0,5)=0,5 
ve 
=0,46 ve S=0,498 olur. Şayet tüm İstanbul halkını örnek
olarak alsa idik bu iki kesikli dağılım birbirinin aynisi olacaktı. n=100 için
örnek dağılımımızda kesikli. MLT den biliyoruzki 
n>30 için 
be a sample proportion found defective by the quality
assurance test.